Direction vectors are d1=(1,2,2) with magnitude 3, and d2=(3,2,6) with magnitude 7. Dot product =3+4+12=19. So cosθ=19/(3⋅7)=19/21, giving θ=cos−1(19/21).
The angle between the lines = 3 i + 2 j - 4 k + λ( i + 2 j + 2 k) and = 5 j - 2 k + μ(3 i + 2 j + 6 k) is :
CUET UG 2023 — Mathematics Geometry
2023mcqmedium
The angle between the lines r=3i^+2j^−4k^+λ(i^+2j^+2k^) and r=5j^−2k^+μ(3i^+2j^+6k^) is :
Official previous-year question
Held on 23 May 2023 · Verified 13 Jul 2026.
Options
- A
sin−1(2119)
- B
cos−1(2319)
- C
cos−1(2119)
- D
sin−1(2319)
Did you get this right?
Sign in to track your attempts and accuracy.
Your note
Sign in to keep a private note on this question. Nothing you write is ever public.
CUET UG Geometry in other years
More CUET UG Geometry questions
Consider $f(x) = \sin(3x) + 4, \forall x \in \mathbb{R}$. Then (A) Maximum value of $f(x)$ is 5 (B) Minimum value of $f(x)$ is 3 (C) Maximum value of $f(x)$ is attained at $x = \frac{\pi}{6}$ (D) Minimum value of $f(x)$ is attained at $x = 0$ Choose the correct answer from the options given below:
2025medium
The maximum value of $\sin x \cdot \cos x$ is:
2025easy
The angle between the pair of lines given by $\vec{r} = \hat{i} + 2\hat{j} - 3\hat{k} + \lambda (\hat{i} - 2\hat{j} + 2\hat{k})$ and $\vec{r} = 5\hat{i} + \hat{j} + \hat{k} + \mu (3\hat{i} - 2\hat{j} + 6\hat{k})$ is
2025medium
The minimum value of the function $f(x) = 3\sin x - 4\cos x, x \in [-4\pi, 4\pi]$ is equal to
2025medium
Acute angle between the lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{5}$ and $\frac{x-1}{4} = \frac{y+1}{-3} = \frac{z+10}{5}$ is:
2025medium
Other Mathematics topics for CUET UG
Keep practicing Geometry
Work through every CUET UG Geometry PYQ, year by year.